Roesler, Mathias · University of Auckland Data Repository · 2024
<b>Structure tensor validation</b><b>General information</b>This item contains test data to validate the structure tensor algorithms and a supplemental paper describing how the data was generated and used. <b>Contents</b>The <b>test_data.zip</b> archive contains 101 slices of a cylinder (701x701 pixels) with two artificially created fibre orientations. The outer fibres are oriented longitudinally, and the inner fibres are oriented circumferentially, similar to the ones found in the rat uterus. The <b>rat_uterus_texture_validation.pdf</b> file is a short supplemental paper describing the generation of the test data and the results after being processed with the structure tensor code.
Cited by 0Open access
Grey Ballard, Tamara G. Kolda · Cambridge University Press eBooks · 2025
Cited by 0
2013
Abstract — We consider image denoising as the problem of removing spurious oscillations due to noise while preserving edges in the images. We will suggest here how to directly make infinitesimal adjustment to standard variational methods of image denoising, to enhance desirable target assumption of the noiseless image. The standard regularization method is used to define a suitable energy functional to penalize the data fidelity and the smoothness of the solution. This energy functional is tailored so that the region with small gradient is isotropically smoothed whereas in a neighborhood of an edge presented by a large gradient smoothing is allowed only along the edge contour. The regularized solution that arises in this fashion is then the solution of a variational principle. To this end the associated Euler — Lagrange equation needs to be solved numerically and the half-quadratic minimization is generally used to linearize the equation and to derive an iterative scheme. We describe here a method to modify Euler — Largrange equation from commonly used energy functionals, in a way to enhance certain desirable preconceived assumptions of the image, such as edge preservation. From an algorithmic point of view, we may deem this algorithm as a smoothing by a local average with an adaptive gradient-based weight. However, this algorithm may result in noisy edges although the edge is preserved and noise is suppressed in the low-gradient regions of the image. The main focus here is to present an edge-preserving regularization in the aforementioned view point, and to provide an alternative and simple way to modify the existing algorithm to mitigate the phenomena of noisy edges without explicitly defining step where we specify an energy functional to be minimized.
Cited by 0
Grey Ballard, Tamara G. Kolda · Cambridge University Press eBooks · 2025
Cited by 0
Kumano, S. · arXiv (Cornell University) · 2014
We explain spin structure for a spin-one hadron, in which there are new structure functions, in addition to the ones ($F_1$, $F_2$, $g_1$, $g_2$) which exist for the spin-1/2 nucleon, associated with its tensor structure. The new structure functions are $b_1$, $b_2$, $b_3$, and $b_4$ in deep inelastic scattering of a charged-lepton from a spin-one hadron such as the deuteron. Among them, twist-two functions are related by the Callan-Gross type relation $b_2 = 2 x b_1$ in the Bjorken scaling limit. First, these new structure functions are introduced, and useful formulae are derived for projection operators of $b_{1-4}$ from a hadron tensor $W_{μν}$. Second, a sum rule is explained for $b_1$, and possible tensor-polarized distributions are discussed by using HERMES data in order to propose future experimental measurements and to compare them with theoretical models. A proposal was approved to measure $b_1$ at the Thomas Jefferson National Accelerator Facility (JLab), so that much progress is expected for $b_1$ in the near future. Third, formalisms of polarized proton-deuteron Drell-Yan processes are explained for probing especially tensor-polarized antiquark distributions, which were suggested by the HERMES data. The studies of the tensor-polarized structure functions will open a new era in 2020's for tensor-structure studies in terms of quark and gluon degrees of freedom, which is much different from ordinary descriptions in terms of nucleons and mesons.
Cited by 0Open access
Hao Huang, Marina Bentivoglio, Matthew D. Budde et al. · 2015
Diffusion tensor imaging (DTI) and tractography offer the unique possibility to visualize the developing white matter macroanatomy of the human fetal brain in vivo and in utero and are currently under investigation for their potential use in the diagnosis of developmental pathologies of the human central nervous system. However, in order to establish in utero DTI as a clinical imaging tool, an independent comparison betweenmacroscopic imaging and microscopic histology data in the same subject is needed. The present study aimed
Cited by 0
Niels Jeppesen, rdengate · Zenodo (CERN European Organization for Nuclear Research) · 2024
Fixed bug when using a sliced numpy.memmap with parallel_structure_tensor_analysis. Full Changelog: https://github.com/Skielex/structure-tensor/compare/v0.3.0...v0.3.1
Cited by 0Open access
Rodrigo Morelatto, Ricardo Biloti · 2013
The structure tensor is a very versatile tool used in general image processing. It can be used to detect edges, estimate coherency and local slopes. In this work we employ the structure tensor to estimate local slopes. We compare the slopes obtained by this tool with the slopes obtained by plane-wave destruction filters. Those two methods were tested against a synthetic and a real dataset. The slopes detected through the structure tensor were reliable and comparable to the ones obtained with plane-wave destruction filters. Finally, we present an application for the slopes detected by the structure tensor. We show how to employ them to filter seismic data along structures.
Cited by 3
Alvaro Arias, Jeff D. Farmer · 1994
We examine some structural properties of (injective and projective) tensor products of ℓp-spaces (projections, complemented subspaces, reflexivity, isomorphisms, etc.). We combine these results with combinatorial arguments to address the question of primarity for these spaces and their duals.
Cited by 0
Anandam Banerjee · Journal of K-theory K-theory and its Applications to Algebra Geometry and Topology · 2011
Abstract Recently, Bondarko constructed a DG category of motives, whose homotopy category is equivalent to Voevodsky's category of effective geometric motives, assuming resolution of singularities. Soon after, Levine extended this idea to construct a DG category whose homotopy category is equivalent to the full subcategory of motives over a base-scheme S generated by the motives of smooth projective S -schemes, assuming that S is itself smooth over a perfect field. In both constructions, the tensor structure requires ℚ-coefficients. In this article, it is shown how to provide a tensor structure on the homotopy category mentioned above, when S is semi-local and essentially smooth over a field of characteristic zero. This is done by defining a pseudo-tensor structure on the DG category of motives constructed by Levine, which induces a tensor structure on its homotopy category.
Cited by 3
Deqiang Yang, Zhi-xia Ye, Yang Zhao et al. · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2011
Face recognition has broad applications, and it is a difficult problem since face image can change with photographic conditions, such as different illumination conditions, pose changes and camera angles. How to obtain some invariable features for a face image is the key issue for a face recognition algorithm. In this paper, a novel tensor structure of face image is proposed to represent image features with eight directions for a pixel value. The invariable feature of the face image is then obtained from gradient decomposition to make up the tensor structure. Then the singular value decomposition (SVD) and principal component analysis (PCA) of this tensor structure are used for face recognition. The experimental results from this study show that many difficultly recognized samples can correctly be recognized, and the recognition rate is increased by 9%-11% in comparison with same type of algorithms.
Cited by 1
Anandam Banerjee · 2010
Grothendieck first defined the notion of a "motif" as a way of finding a universal cohomology theory for algebraic varieties. Although this program has not been realized, Voevodsky has constructed a triangulated category of geometric motives over a perfect field, which has many of the properties expected of the derived category of the conjectural abelian category of motives. The construction of the triangulated category of motives has been extended by Cisinski-Deglise to a triangulated category of motives over a base-scheme S. Recently, Bondarko constructed a DG category of motives, whose homotopy category is equivalent to Voevodsky's category of effective geometric motives, assuming resolution of singularities. Soon after, Levine extended this idea to construct a DG category whose homotopy category is equivalent to the full subcategory of motives over a base-scheme S generated by the motives of smooth projective S-schemes, assuming that S is itself smooth over a perfect field. In both constructions, the tensor structure requires coefficients. In my thesis, I show how to provide a tensor structure on the homotopy category mentioned above, when S is semilocal and essentially smooth over a field of characteristic zero. This is done by defining a pseudo-tensor structure on the DG category of motives constructed by Levine, which induces a tensor structure on its homotopy category.
Cited by 1Open access
G. Savvidy · Theoretical and Mathematical Physics · 2015
Cited by 2Open access
Barbieri-Viale, Luca, Huber, Annette, Prest, Mike · arXiv (Cornell University) · 2018
We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.
Cited by 0Open access
Seyyid Emre Sofuoglu, Selin Aviyente · IEEE Transactions on Image Processing · 2021
Higher-order data with high dimensionality arise in a diverse set of application areas such as computer vision, video analytics and medical imaging. Tensors provide a natural tool for representing these types of data. Two major challenges that confound current tensor based supervised learning algorithms are storage complexity and computational efficiency. In this paper, we address these problems by introducing a multi-branch tensor network structure. The multi-branch structure is a general tensor decomposition that includes Tucker and tensor-train (TT) as special cases and takes advantage of the flexibility of the tensor network to provide a better balance between storage and computational complexity. We then introduce a supervised discriminative tensor-train subspace learning approach referred to as tensor-train discriminant analysis (TTDA), and its implementations using the multi-branch tensor network structure. Multi-branch implementations of TTDA are shown to achieve lower storage and computational complexity while providing improved classification performance with respect to both Tucker and TT based supervised learning methods.
Cited by 1Open access
Luca Terenzi · Annals of K-Theory · 2026
Let $k$ be a field of characteristic $0$ endowed with a complex embedding $σ: k \hookrightarrow \mathbb{C}$. In this paper we complete the construction of the six functor formalism on perverse Nori motives over quasi-projective $k$-varieties, initiated by Ivorra--Morel. Our main contribution is the construction of a closed monoidal structure on the derived categories of perverse Nori motives, compatibly with the analogous structure on the underlying constructible derived categories. This is based on an alternative presentation of perverse Nori motives, related to the conjectural motivic perverse $t$-structure on Voevodsky motivic sheaves. As a consequence, we obtain well-behaved Tannakian categories of motivic local systems over smooth, geometrically connected $k$-varieties. Exploiting the relation with Voevodsky motivic sheaves in its full strength, we are able to define Chern classes in the setting of perverse Nori motives, which leads to a motivic version of the relative Hard Lefschetz Theorem.
Cited by 4Open access
Maider Marin-McGee, Miguel Vélez-Reyes · 2011
In this article, a structure tensor for hyperspectral images (HSI) is proposed. A weighted zero mean smoothed gradient to calculate the initial matrix field is used. The weights are constructed from the zero mean data by comparison with a normalized absolute value of the median. The problem with the classical definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result many non-edge pixels are reinforced producing false edges. Therefore, other processes that depend on the structure tensor will be misguided. The proposed weights are selected from pixel's spectral values that are greater than and closely around the absolute value of the median, reinforcing only the better candidates in the spectra to be edges in their respective spectral interval, therefore making the structure tensor a better edge discriminator. Comparisons of this method with the standard definition of the structure tensor and results of using the proposed method for nonlinear tensor anisotropic diffusion are presented.
Cited by 6
SÉRGIO DE ANDRADE, PAULO · Zenodo (CERN European Organization for Nuclear Research) · 2025
Finite tensor categories represent a profound generalization of algebraic structures, bridging concepts from representation theory of finite groups and algebras to quantum field theory and low-dimensional topology. This paper provides an extensive review of the structure theory of finite tensor categories, emphasizing their fundamental definitions, key properties, and the powerful tools employed in their analysis and classification. We delve into their foundational components, including their monoidal structure, semisimplicity, rigidity, and the role of Frobenius-Perron dimensions in characterizing their behavior. A significant portion of this work is dedicated to exploring pivotal structural results such as the classification of pointed tensor categories, the properties of the Grothendieck ring or fusion ring, and the profound implications of the Drinfeld center construction. Furthermore, we discuss the intricate connections between finite tensor categories and other areas of mathematics and physics, including quantum groups, subfactor theory, and vertex operator algebras. The methodology section details the mathematical techniques essential for this study, such as module categories and group theoretical approaches. Finally, we synthesize these results, offering insights into open problems and future research directions, underscoring the enduring significance of finite tensor categories as a vibrant area of contemporary mathematical research.
Cited by 0Open access
Adib Akl, Joe Iskandar · 2015
Texture analysis has been a particularly dynamic field with different computer vision and image processing applications. Most of the existing texture analysis techniques yield to significant results in different applications but fail in difficult situations with high sensitivity to noise. Inspired by previous works on texture analysis by structure layer modeling, this paper deals with representing the texture's structure layer using the structure tensor field. Based on texture pattern size approximation, the proposed algorithm investigates the adaptability of the structure tensor to the local geometry of textures by automatically estimating the sub-optimal structure tensor size. An extension of the algorithm targeting non-structured textures is also proposed. Results show that using the proposed tensor size regularization method, relevant local information can be extracted by eliminating the need of repetitive tensor field computation with different tensor size to reach an acceptable performance.
Cited by 8
Ahmadreza Baghaie, Zeyun Yu · AEU - International Journal of Electronics and Communications · 2014
Cited by 44Open access